Scaling in Damage Accumulation

  • L.R. Botvina
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


A detailed analysis of damage accumulation in metal specimens under irradiation, tension, mechanical and thermal fatigue shows that it occurs in two stages, the first being dominated by defect accumulation and the second, by defect growth. The stages are characterized by different sensitivity of defects to material structure and different defect size distributions. During the first stable stage, when most defects do not exceed the grain size, the defects initiate, grow and are blunted on reaching the maximum density determined by loading conditions and material structure. The cumulative number – size distributions of defects at this stage are described by exponential laws. The next stage is that of accumulation of defects of the next hierarchical level and transition to this stage occurs by coalescence of defects of the preceding level. The patterns of defects are self-similar. Formation of propagating microcracks whose length is significantly larger than the grain size leads to initiation of the accelerated stage of damage development which is described by a power–like cumulative size – frequency distribution of defects. The slope of this distribution decreases with load and fractal dimension of the damage patterns which form under tension and cyclic loading. The study of evolution of localized plastic zones at different loading stages shows that the size of the plastic zone may be considered to be the correlation length of the damage accumulation process. Analysis of damage process in terms of phase transition theory allowed us to suppose that the above-mentioned stages can be related to the self-organized criticality of accumulation of non-propagating defects and to the criticality due to a macrocrack formation.


Self-similarity damage accumulation plastic deformation zone fractal dimension defect distribution by size acoustic emission 


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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • L.R. Botvina
    • 1
  1. 1.Institute of Metallurgy and Material SciencesRussian Academy of SciencesRussia

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